I don't believe there is a timing adjustment on the Kohler Magnum. It uses an ignition module mounted next to the flywheel, it's fixed. You might be losing spark intermittently and when it fires it's igniting that unburned fuel or maybe lost spark on one side.
I have a couple of cheap Harbor freight spark indicators that work great for these kind of problems. Hook em up inline with the spark plug, tells you immediately if it's a spark problem.
This module has a ground through the ignition switch, it grounds to kill spark.
The control for that is entering the same location as the plug wire through the sheet metal on the engine case.
I've replaced two of those module in 20 years, hope it's something simpler like a carb issue!
Curt